1. Field of the Disclosure
The field of disclosure relates to the production of hydrocarbon-based fluids. More specifically, the disclosure relates to a method for determining the water cut value for increasing the production of hydrocarbons from a reservoir, including enhanced oil recovery (EOR).
2. Description of the Related Art
The challenges associated with increasing the production of hydrocarbons such as crude oil in maturing production fields are well-established in the oil and gas industry. One solution for achieving EOR involves the use of water injection techniques, which can enhance the production of a reservoir by up to 50%. However, the use of water injection or “water cut” techniques can become economically unfeasible when a significant proportion of water is present relative to the corresponding volume of hydrocarbon, such as 80% water/20% hydrocarbon or greater. It would therefore be advantageous to develop accurate and informative methods for determining water and hydrocarbon ratios capable of both maximizing EOR and accounting for additional fluid, physicochemical conditions, and reservoir conditions, including but not limited to salinity and temperature.
It is known that when two materials, such as a hydrocarbon and water, with different permittivity values (∈1 and ∈2) are mixed together that the resulting mixture permittivity (∈m) is either ∈m<<both ∈1 and ∈2 or ∈m>>both ∈1 and ∈2. See S. Beer et al. “In-Line Monitoring of the Preparation of Water-in-Oil-in-Water (W/O/W) Type Multiple Emulsions via Dielectric Spectroscopy”, Int. J. Pharm. 441 (2013) pp. 643-647 (hereinafter “Beer”). As described in Beer, evidence for the real presence of such a phenomenon is presented by a relative permittivity of 400 measured in conductive a W/O/W emulsion even though none of the individual components of the emulsion had a permittivity exceeding 80. In the case of a water-in-oil dual-phase fluid—a combination of two incompatible fluids that is often encountered downhole as part of a produced hydrocarbon-based composition—differences in mixture permittivity (∈m) versus the real component of permittivity of either brines and crude oil alone is predicted to be a consequence of the presence of greater conductivities in the minority phase, which is brine or formation water. The greater conductivity of the minority phase manifests itself as the imaginary component to the detected permittivity of the mixture. See Sihvola, “Homogenization Principles and Effect of Mixing on Dielectric Behaviour”, Photon. Nanostruct: Fundam. Appl. (2013).
Reduced frequency (≤1 MHz) permittivity measuring devices are based upon detecting the capacitance of a fluid. Two of the most applied models which are used to estimate ∈m in such devices are variants of the Maxwell Garnet formula and the model proposed by D. A. G. Bruggeman. See C. Maxwell Garnet, “Colours in Metal Glasses and Metal Films,” Trans. of the Royal Soc. (London) 203 (1904) pp. 385-420; D. A. G. Bruggeman, “Berechnung verschiedener physikalisches Konstanten von heterogenen Subtanzen. I. Dielektrizitätskonstanten and Leitfähigkeiten der Mischkörper aus isotropen Substanzen”, Annalen der Physik 24 (7-8) (1935) pp. 636-679 (hereinafter “Bruggeman”).
Permittivity measuring devices are often calibrated with the assumption that the imaginary permittivity component of the fluid being tested does not provide a substantial contribution to detected mixture permittivity. This results in an assumption that the determined mixture permittivity behaves in a monotonic-type manner behavior as a function of increasing water cut (α). The water cut value for a composition is the ratio of the amount of the aqueous portion of a composition to the amount of the non-aqueous portion, for example the hydrocarbon portion, where “0” represent a pure non-aqueous material and “1” represents a pure aqueous material. Water cut can be characterized as having a range of from 0 (no water) to 1 (all water).
The large imaginary component of permittivity, which originates from a greater-conductivity minority phase in the oil/water dual-phase fluid, can manifest itself as part of the mixture permittivity value. As outlined in Beer and in K. Kupfer (ed.), Electromagnetic Aquametry, Ch. 5, A. Sihvola “Model Systems for Materials with High Dielectric Losses in Aquametry”, Springer, Heidelberg (2005) pp. 93-112, the inclusion of such a greater conductivity as a factor in mixture permittivity value (∈m) results in what is characterized as non-monotonic behavior.
If one was to use the Bruggeman model and solve for the mixture permittivity value (Cm), the solution to the Bruggeman model that describes an even distribution of water droplets (an assumption for a minority phase of water evenly distributed in a majority phase of non-water) can be expressed as follows:∈m=¼(2∈1−3α∈1−∈2+3α∈2+√{square root over (8∈1∈2+(2∈1−3α∈1−∈2+3α∈2)2)})  (Equation 1).
For a combination of hydrocarbons such as crude oil and water, solving for the permittivity value of pure crude oil is relatively easy. The real component of permittivity of a fluid is understood to be a measure of how much energy from an external electric field is stored in a material. Oil is generally assumed not to be conductive, so there are no energy losses from the fluid. Because there is no energy loss from the fluid acting as a capacitor, there no imaginary component of permittivity for a hydrocarbon fluid. The real component of permittivity value of crude oil (Re[∈crude_oil]), which is also the permittivity of crude oil (∈crude_oil), is equal to 3.
The determination of the complex permittivity of brine requires a more sophisticated calculation. The imaginary component of permittivity is associated with the conductivity of the material. Conductivity of a material is shown as the loss of energy from a material as energy is conveyed through the material instead of retained. Using a sodium chloride (NaCl) brine having a concentration of about 200,000 ppm NaCl (mass) at a temperature of 90° C., the conductivity of the brine (σbrine) is about 50 S/m (Siemens/meter). A salinity value is the amount of dissolved salts in the composition in parts-per-million (ppm mass). The determined real permittivity component value of the brine (Re[∈brine]) is about 50, which induces a frequency (f) of about 10,000 Hz (a reduced frequency) into the brine to produce a mixture permittivity (∈brine) that allows for the empirical determination of the imaginary component of permittivity via back-calculation.
The calculation of the imaginary component of the permittivity of a brine (χbrine) with a known conductivity at a given frequency can also be performed using the following expression:
                                          𝒳            brine                    =                                                    σ                brine                                            2                ⁢                                  πɛ                  0                                ⁢                f                                      =                          8.99              ×                              10                7                                                    ,                            (                  Equation          ⁢                                          ⁢          2                )            where ∈0=8.85×10−12 F/m (Farad/meter), which is the known as the permittivity of free space. The calculated complex permittivity of the brine is:∈brine=Re[∈brine]+iχbrine=50+8.99×107i  (Equation 3).
FIG. 1 is a graph showing the relationship between the determined permittivity of a hydrocarbon-and-brine composition on a logarithmic scale (log10(Re[∈mix]) to its water cut value by introducing both an oil and a complex water permittivity functions (including Equation 3) into the Bruggeman model (Equation 1) (solid line) and by using a commercially-available water cut sensor that uses an approximation of the Bruggeman model (dashed line). The testing frequency and salinity are fixed at the previously stated values (10,000 Hz and 50 S/m) while the water cut value is modified to produce the determined mixture permittivity. The water cut values range from 0 (100% hydrocarbon) to a value of 0.5 (50:50 hydrocarbon:brine).
As shown in FIG. 1, the presence of greater levels of conductance in the brine phase result in the presence of the non-linear peak for the determined real permittivity of the mixture that is in a range of from about 0.3 to about 0.4 for the water cut value (α). The magnitude of the detected peak in mixture permittivity is about 100,000,000 (log10=8), which is a value that exceeds the maximum real permittivity component values for either brine or crude oil (∈=about 50 and 3, respectively). The large imaginary component of brine permittivity in this range suggests that the imaginary component cannot be ignored when determining the mixture permittivity of a dual-phase composition, especially one with a minor phase that is conductive, unlike what commercial permittivity sensors can determine.
The other problem of using a method that relies on the assumption of a monotonic curve relationship for determining mixture permittivity is shown in FIG. 2. The existence of non-monotonic deviations in the determined mixture permittivity results in spurious “spikes”, amplifications or “signal-doubling” of the determined permittivity mixture values. FIG. 2 is a graph showing the relationship between the determined permittivity of the mixture when the value of the water cut (α) is rapidly varied by 5% with time within the water cut value range of α=0.3 to 0.4, such as what would happen in a continuous production process of a crude oil-and-water composition. The signal-doubling occurs because the water cut value is varied across the peak of the determined mixture permittivity shown in FIG. 1. Such oscillations in mixture permittivity could lead a person of skill in the art to incorrectly conclude that dramatic water or brine slugging is occurring. The Bruggemann model, when used with complex crude oil and water permittivity functions, predicts such rapid increases in the mixture permittivity even with minor variations in the overall oil:brine ratio in the composition.
Depending on the model used to describe the permittivity function with relationship to salinity, frequency and water cut, or to the permittivity value of the mixture where the variables are fixed, different non-linear dependencies are encountered. Such non-linearity effects are only observed where the salinity of the brine is great enough to result in a conductivity that drives the imaginary component of permittivity to overwhelm both the real permittivity of the brine and the crude oil. The presence of such non-linear effects in a downhole hydrocarbon and conductive brine composition can be regarded as an example of a dielectric meta-material (where two or more dielectrics are arranged in a regular fashion). Just as excessive permittivity for a composition can be induced beyond each component's relative permittivity, losses due to excessive conductivity can be induced in a dielectric meta-material where neither component has any loss properties.
It is therefore desirable to be able to account for large non-linear effects of conductivity in the minor phase of a dual-phase fluid, such as a crude oil-brine composition. It is also useful to determine an estimate of the water cut value for the crude oil-brine composition based upon empirical or theoretical models that account for the imaginary components of mixture permittivity whether certain variables, including salinity value, are known or not.